If a verification ver is given, then boolean acts as a filter, converting anything returned by verify into either true, false, or FAIL.

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The verification truefalse makes one further change, converting any FAIL results into false.

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These are useful in case the result from verify is to be used as input to another procedure such as sort or select.

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The verifications boolean and truefalse are symmetric and a verification boolean(ver) is symmetric if and only if the verification ver is symmetric. If a verification ver is symmetric, then this implies that the verification truefalse(ver) is symmetric.